Question

A forma simplificada da fração 2x-4/x²-4x+4 + x²+2x+1/x²-1

Answer 1

$\dfrac{2x-4}{x^2-4x+4} + \dfrac{x^2+2x+1}{x^2-1}\\\\ para\ x^2-4x+4\\ Delta=16-16=0\\\\ x= \dfrac{4}{2*1}\\\\ x= 2\\\\ para\ x^2+2x+1\\ Deta=4-4=0\\\\ x= \dfrac{-2}{2*1}\\\\ x=-1\\\\\\ \dfrac{2x-4}{x^2-4x+4} + \dfrac{x^2+2x+1}{x^2-1}\\\\ \dfrac{2(x-2)}{(x-2)(x-2)} + \dfrac{(x+1)(x+1)}{(x+1)(x-1)}\\\\ \dfrac{2}{x-2} + \dfrac{x+1}{x-1}\\\\ \dfrac{2(x-1)+(x+1)(x-2)}{(x-2)(x-1)} }\\\\ \dfrac{2x-2+x^2-2x+x-2}{(x-2)(x-1)} }\\\\ \dfrac{x^2+x-4}{(x-2)(x-1)} }$